230. Kth Smallest Element in a BST

Given a binary search tree, write a function kthSmallest to find the kth smallest element in it.

Note:
You may assume k is always valid, 1 ≤ k ≤ BST's total elements.

Example 1:

Input: root = [3,1,4,null,2], k = 1
3
/
1 4

2
Output: 1

Example 2:

Input: root = [5,3,6,2,4,null,null,1], k = 3
5
/
3 6
/
2 4
/
1
Output: 3

Follow up:
What if the BST is modified (insert/delete operations) often and you need to find the kth smallest frequently? How would you optimize the kthSmallest routine?

# Definition for a binary tree node.
class TreeNode:
    def __init__(self, x):
        self.val = x
        self.left = None
        self.right = None

class Solution:
    def kthSmallest(self, root, k):
        """
        :type root: TreeNode
        :type k: int
        :rtype: int
        """
        ans = []
        def inorder(root):
            if root.left:
                inorder(root.left)
            ans.append(root.val)
            if root.right:
                inorder(root.right)
        inorder(root)
        return ans[k-1]